Texas A&M University (TAMU) MATH 367 Structure of Mathematics III Test 1 Practice

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• Which statement correctly describes a subset relation?
• Which symbol denotes the negation of a single proposition p?
• Which statement is a correct De Morgan law for complements of unions and intersections?
• Which classification of a triangle has all three sides congruent?
• Which statement correctly defines an injective function?
• Which of the following is the correct De Morgan’s law for the complement of a union and an intersection?
• Incidence axiom 3 restated: If P and Q lie in plane E, then line PQ is a subset of E.
• A right angle is defined as an angle whose measure is:
• What is the union of ray AB and ray BA?
• Is divisibility relation on positive integers a partial order? Provide justification.
• What does the Vertical Angles Theorem assert?
• Which condition characterizes a subset A of a universal set U?
• Incidence axiom 2 states that how many noncollinear points determine a plane?
• What is the contrapositive of p → q?
• Which expression is logically equivalent to p implies q?
• What is the truth value of p-->q when p is false and q is true?
• Which of the following are the undefined terms of the axiomatic system?
• Which statement correctly describes an isosceles triangle?
• From the statement 'It is raining, then it is Monday', select the Contrapositive.
• Segment Construction Theorem: For AB and ray CD, which description correctly describes the theorem?
• Which statement expresses the supplement postulate?
• In a function f: H -> K, which is the domain?
• According to the incidence axioms, which statement about two points and a line is true?
• What is the truth value of p-->q when p is true and q is true?
• Let A, B, C be collinear. If AB + BC = AC, which statement must be true?
• Which expression is equal to the complement of the complement of A with respect to a universal set U?
• Which statement is true about the SAS postulate’s conclusion when two triangles satisfy its conditions?
• Which statement correctly distinguishes a valid argument from a sound argument?
• If f∘g is injective, what can be concluded about g?
• Suppose A and B are finite sets with A ∩ B = ∅. What is |A ∪ B|?
• Which statement about the null set is true?
• Which of the following numbers is the sum of the digits of 15?
• Which statement is the contrapositive of the generic form 'If p then q'?
• If two angles have the same measure, what can be concluded about their congruence?
• Which statement about a line is always true?
• Which description defines triangle ABC?
• In Cantor’s diagonal argument, which statement best describes why the diagonal set S is a problem for surjectivity?
• In a proof by contradiction, which assumption is made to derive a contradiction?
• Which statement correctly captures the relationship between injectivity and left inverses?
• What best describes axioms (postulates) in this system?
• Which statement characterizes a bijection?
• Which of the following is not an indirect proof method?
• Which statement best defines an equivalence relation?
• Which describes the ray AB?
• Which relation on the integers is a classic example of an equivalence relation?
• Which expression represents the conjunction of two propositions p and q?
• For finite sets A and B with |A|=m, |B|=n, and |A∩B|=k, what is |A∪B|?
• Which of the following are defined terms in the axiomatic system?
• What is the null (empty) set?
• What is the complement A^c with respect to a universal set U?
• Which properties show that ⊆ on P(S) is a partial order?
• What is the negation of the statement 'Some days are not sunny'?
• If A, B, C are collinear with B between A and C, which equality must hold?
• Segment Construction Theorem: Given segment AB and ray CD, there is exactly one point E on ray CD such that AB ≅ CE. Which statement describes this theorem?
• Given A = {1,2,4,7,9} and B = {2,5,7,8}, which is A ∩ B?
• Which statement is false?
• The composition of two injective functions is:
• What is the inverse of the statement 'If it is raining, then it is Monday'?
• In a function notation f: H -> K, which statement about the domain is true?
• Which of the following is not an undefined term in the axiomatic system?
• Which statement expresses the reason for the formula |A∪B| = |A|+|B|−|A∩B|?
• Which statement about vertical angles is true?
• Which statement is always true about A and its complement A^c?
• If A, B, C are collinear and AB = BC, what can be concluded about B with respect to A and C?
• Given A = {1,2,4,7,9} and B = {2,5,7,8}, which is A ∪ B?
• Which statement is guaranteed by the ruler postulate?
• Which number is a valid counterexample to the statement: If the sum of the digits of a number is divisible by 6, then the number is divisible by 6?
• Which of the following statements about the Cantor pairing function is true?
• According to incidence axiom 2, how many noncollinear points are required to determine a plane?
• An angle is best described as:
• From the statement 'It is raining, then it is Monday', select the Converse.
• Which statement is guaranteed for every finite nonempty partially ordered set (poset)?
• Which statement is a valid characterization of the subset relation ⊆ on P(S)?
• Which of the following is NOT a valid triangle congruence postulate?
• Suppose f is an injection from a finite set X to itself. Which statement must be true?
• Given A = {1,2,4,7,9} and B = {2,5,7,8}, which is A - B?
• If A ⊆ B and B ⊆ A, what can we conclude?
• If two angles form a linear pair, what can we say about their measures?
• In a direct proof of P-->Q, what is the standard sequence?
• Let a_n satisfy a_n = 2 a_{n-1} with a_0 = 1. What is the closed-form expression for a_n?
• If p is true and q is false, what is the truth value of the disjunction p V q?
• In the context of proving P-->Q, which option is not a standard move in a direct proof?
• In the induction step for the sum 1+2+...+n = n(n+1)/2, if S_n denotes the sum to n, which equation expresses S_{n+1}?
• Which is the power set of {1,2}?
• What is another standard name for the null set?
• An obtuse angle has a measure that is:
• According to the incidence axiom discussed, if two distinct planes intersect, their intersection is which geometric object?
• Line segment AB is defined as which of the following?
• Which statement correctly describes the power set P(S)?
• Negation of the statement ‘Sue works or goes to school every day’ is which of the following?
• Let A1, A2, ..., Ak be finite sets. Which statement correctly justifies that their union is finite?
• Which of the following is a bijection from a two-element set to a two-element set?
• Negation of the statement ‘John is tall and has black hair’ is which of the following?
• In proving P implies Q by contrapositive, which implication is proved directly?
• Which statement best captures the goal of a direct proof of P-->Q?
• If two planes are parallel, their intersection is which of the following?
• A triangle with no sides congruent is called what?
• Which statement describes a triangle with exactly two equal sides?
• If a set S has n elements, how many elements does its power set P(S) have?
• Which properties must hold for ≤ on the integers to be a partial order?
• In the HL postulate, which parts must be congruent to conclude triangle congruence for right triangles?
• In a proof by contradiction, what does deriving a contradiction show about the assumed scenario P and not Q?
• Which expression represents the disjunction of two propositions p and q?
• If AB = CD, what can be concluded about segments AB and CD?
• Which statement correctly reflects the incidence axiom for two planes?
• Which half-planes define the interior of triangle ABC?
• Which statement is true about supplementary angles?
• HL postulate applies to which type of triangles?
• From the statement 'It is raining, then it is Monday', select the Inverse.
• What is the contrapositive of the statement 'If it is raining, then it is Monday'?
• An acute angle is an angle with measure:
• In the angle-angle-side postulate, which configuration guarantees congruence of two triangles?
• Negation of the statement ‘Every dog has four legs’ is which of the following?
• If p is true and q is false, what is the truth value of the conjunction p^q?
• Which expression denotes the implication from p to q?
• In triangle ABC, given a point P, P is inside angle ABC precisely when P and A lie on the same side of line BC and P and C lie on the same side of line AB. Which option matches this condition?
• Which statement defines the ASA congruence criterion?
• Which property must hold for an injective function?
• In Cantor's diagonal argument, which property of the constructed set S leads to a contradiction with assuming surjectivity?
• If f∘g is surjective, what can be concluded about f?
• What is the Cantor pairing function π(x,y) that provides a bijection N×N→N?
• State Euclid's lemma: If p is prime and p divides ab, what must be true?
• If f: A→B is bijective, which statement about its inverse f^{-1}: B→A is true?
• When proving by induction that 1+2+...+n = n(n+1)/2, what is the base case?
• State the Fundamental Theorem of Arithmetic.
• Incidence axiom 3 says that if P and Q lie in plane E, then what can be said about line PQ?
• Describe the disjoint union A⊔B and its cardinality.
• Two angles are supplementary if their measures sum to:
• Which statement correctly describes the SAS postulate?
• Given a bijection f: A→B, the inverse function f^{-1}: B→A is always:
• Which of the following describes a contrapositive proof for P-->Q?
• What does A ∩ B denote in set notation?
• What is the intersection of ray AB and ray BA?
• ASA postulate states that two angles and which side determine triangle congruence?
• Which method of proving P implies Q requires assuming P is true and showing Q must follow?